Question

tanA+cotA=2 then find the value of tan3A+cot3A=?

Answer 1

Answer:

tan3A+cot3A = -2

Step-by-step explanation:

tanA+cotA=2

=> SinA/CosA  + CosA/SinA  = 2

=> Sin²A  + Cos²A = 2CosASinA

=> 1 = Sin2A

=> 2A = 90°

=>   A = 45°

tan3A+cot3A

= Sin3A/Cos3A  + Cos3A/Sin3A

= (Sin²3A + Cos²3A)/(Cos3ASin3A)

= 2/ (2Cos3ASin3A)

= 2/Sin6A

6A = 6 * 45° = 270

= 2/Sin270

= 2/(-1)

= - 2

tan3A+cot3A = -2